Time-reversal (T/R) communications is a new application area motivated by the recent advances in T/R theory. Although perceived by many in signal processing as simply an application of matched-filter theory, a T/R receiver offers an interesting solution to the communications problem for a reverberant channel. In this paper, the performance of various realizations of the T/R receiver for an acoustic communications experiment in air is described along with its associated processing. The experiment is developed to evaluate the performance of point-to-point T/R receivers designed to extract a transmitted information sequence propagating in a highly reverberant environment. It is demonstrated that T/R receivers are capable of extracting the transmitted coded sequence from noisy microphone sensor measurements with zero-symbol error. The processing required to validate these experimental results is discussed. These results are also compared with those produced by an equivalent linear equalizer or inverse filter, which provides the optimal solution when it incorporates all of the reverberations.

In this paper we present a numerical investigation of reconstructing time-harmonic acoustic pressure field in two dimensional space by using a series expansion—the so-called Helmholtz equation least-squares (HELS) method. Series expansion methods (or the Rayleigh methods) have been widely used in predicting the scatteredacoustic pressure. With regularization, they can also be applied to reconstruction of acoustic pressure on the source surface from the measurements taken in the field, and HELS is the first such attempt for these problems. In this paper, we establish HELS in the framework of the Rayleigh methods and reveal its interrelationship with the Rayleigh hypothesis. In particular, to regularize a reconstruction problem, we use the method of quasisolutions, i.e., a Tikhonov regularization with an a posteriori choice of the regularization parameter. It is shown that without regularization HELS can still yield a satisfactory reconstruction of acoustic radiation from an arbitrary object when enough measurements are taken at sufficiently close range to the source. With regularization the number of measurements can be reduced and reconstruction accuracy be enhanced. It is concluded that HELS can be used to reconstruct acoustic radiation from a convex arbitrarily shaped vibrating object regardless of the validity of the Rayleigh hypothesis, although in practice the results will depend on the rate of convergence of the approximating sequence.

It has been shown previously that the multiple reference and field signals recorded during a scanning acoustical holographymeasurement can be used to decompose the sound field radiated by a composite sound source into mutually incoherent partial fields. To obtain physically meaningful partial fields, i.e., fields closely related to particular component sources, the reference microphones should be positioned as close as possible to the component physical sources that together comprise the complete source. However, it is not always possible either to identify the optimal reference microphone locations prior to performing a holographicmeasurement, or to place reference microphones at those optimal locations, even if known, owing to physical constraints. Here, post-processing procedures are described that make it possible both to identify the optimal reference microphone locations and to place virtual references at those locations after performing a holographicmeasurement. The optimal reference microphone locations are defined to be those at which the MUSIC power is maximized in a three-dimensional space reconstructed by holographic projection. The acoustic pressure signals at the locations thus identified can then be used as optimal “virtual” reference signals. It is shown through an experiment and numerical simulation that the optimal virtual reference signals can be successfully used to identify physically meaningful partial sound fields, particularly when used in conjunction with partial coherence decomposition procedures.